Question

The hiker first travels 200 meters to the east, then 80 meters to the southeast and finally 35 meters to the south. How far is the hiker from his starting point? Give the answer to the nearest ten.

Answer 1

The hiker is approximately 240 meters from the starting point.

Step-by-step explanation:

To find the hiker's distance from the starting point, we need to add up the displacements in each direction. The hiker first traveled 200 meters to the east, which can be represented as a displacement of +200 meters in the x-direction. Then the hiker traveled 80 meters to the southeast, which can be resolved into components of +80*cos(45°) meters in the x-direction and -80*sin(45°) meters in the y-direction. Finally, the hiker traveled 35 meters to the south, which can be represented as a displacement of -35 meters in the y-direction.

To find the total displacement, we add up the x- and y-components. The x-component is 200 + 80*cos(45°) meters and the y-component is -80*sin(45°) - 35 meters. Using trigonometric functions and a calculator, we can find that the x-component is approximately 227.27 meters and the y-component is approximately -89.67 meters.

To find the distance from the starting point (the magnitude of the displacement), we use the Pythagorean theorem. The magnitude of the displacement is sqrt((227.27)^2 + (-89.67)^2) meters, which is approximately 243.61 meters.

Rounding to the nearest ten, the hiker is approximately 240 meters from the starting point.